Abstract
Let G be a finite group. Isaacs and Seitz have conjectured that an upper bound for the derived length of G is the number of irreducible character degrees of G, whenever G is solvable. In this paper, we show that a minimal counterexample to the Isaacs-Seitz conjecture does not contain a non-trivial normal Hall subgroup. On the other hand, Isaacs and Knutson have conjectured that the inequality holds for all solvable normal groups N of G, where . We will prove that this conjecture holds whenever N is a normal Hall subgroup of G and N satisfies the Isaacs-Seitz conjecture.
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